1. Field of the Invention
The present invention relates to a simulation apparatus of a semiconductor device. For example, it relates to an ion implantation simulation apparatus and an ion implantation simulation method especially using the Monte Carlo method.
2. Description of the Related Art
According to the semiconductor TCAD (Technology Computer Aided Design) simulation apparatus which simulates manufacturing processes and electrical characteristics of a semiconductor device, characteristics of a semiconductor are estimated by suitably setting a limited calculation area, by solving an equation based on a physical model with setting up boundary conditions in the calculation area, and by obtaining a structure, an impurities distribution, a carrier distribution, a potential distribution, etc. in the calculation area.
In process simulators for simulating manufacturing processes of the semiconductor device, the Monte Carlo method is sometimes used for simulation of an ion implantation process. In the case of applying the Monte Carlo method to the simulation of an ion implantation process, a prescribed number of particles are implanted into a calculation area at the energy and angle under the implantation conditions, with weighting of ion according to the amount of dose under the implantation conditions. Then, the particles of the prescribed number are tracked until they become in the state of stopping caused by energy loss depending upon interaction with atoms of various substances in the calculation area. Based on a calculation result of the particles of the prescribed number, an impurities concentration distribution, a defect concentration distribution, etc. after the implantation are calculated, and it goes to calculation for a next process.
With respect to ion implantation process simulation, it can be roughly divided into the Monte Carlo method mentioned above and the distribution function method which approximates an ion distribution by an analytic function. Generally, the accuracy of the Monte Carlo method is higher compared to the distribution function method. However, there are a plenty of requests for further accuracy enhancement of the Monte Carlo method. Concerning this point, the technology of accurately simulating concentration distribution at a deep position by performing scattering tests using the Monte Carlo method with gradually changing the weight of the concentration is disclosed, for example, in Japanese Unexamined Patent Publication No. 6-84823.
In the Monte Carlo method, an initial position of an implanted particle is usually set at the spatially highest place in the calculation area randomly, by using uniform random numbers. However, when the condition of implantation is slanting (in the case of slanting implantation), if the initial position is not larger than the calculation area, there will be a portion where no implanted ion reaches on the material surface. Moreover, even under the condition of perpendicular implantation, namely not slanting, particles spilt outside the calculation area because of scattering are not tracked at the end of the calculation area. Thus, the concentration at the end of the calculation may decrease.
For this reason, in the ion implantation simulation using the Monte Carlo method, “reflection type boundary conditions”, indicating when a particle reaches the boundary of the calculation area, the particle rebounds with saving the energy, is sometimes set up as boundary conditions. Moreover, “cycle type boundary conditions”, indicating when a particle reaches the boundary of the calculation area, the particle performs re-incidence from the end of the opposite side of the calculation area with saving momentum to continue the calculation, is also sometimes set up.
However, the “reflection type boundary conditions” may not be appropriate in many cases since the movement direction of the implanted ion is reversed. Further, in the “cycle type boundary conditions”, depending on how to set a calculation area, the calculation area may be incompatible with a device structure being a practical calculation object in many cases.
In such a case, the technology of “extension type boundary conditions” can be introduced as below. That is, different from the above-stated “reflection type boundary conditions” and the “cycle type boundary conditions”, an end structure of the calculation area is extended towards outside the calculation area in order to remove the part where no implanted ion reaches from the original calculation area according to the “extension type boundary conditions”. Moreover, in the technology of the “extension type boundary conditions”, particles spilt outside the original calculation area because of scattering and particles entered from the area extended outside the original calculation area are balanced in order not to cause an unusual concentration fall at the calculation area edge.
When using the technology of this “extension type boundary condition”, it is necessary to suitably determine the size to extend. If the extension width is too large, it takes a long time to calculate a concentration distribution with required accuracy. On the other hand, if the extension width is too small, the concentration distribution at the calculation area edge will become inaccurate. Since required extension sizes are various depending upon implantation conditions, it can be acceptable, for example, to prepare a parameter beforehand and to calculate an extended area based on an ion type, energy, a dose amount, an implantation angle, and a target material, for implantation conditions of a certain range.
However, in the ion implantation calculation using the Monte Carlo method, since these conditions concerning the implantation are very diverse, making a parameter table to determine an extended area beforehand has a scope limit to apply.
As another method, there is a method of actually performing an implantation calculation to obtain an extension width. In this method, a part of total n particles used for the Monte Carlo calculation are utilized for calculating an extension width. Usually, as to the total n particles, about 104 or more particles are used in the implantation calculation even for the one dimensional structure. Therefore, n0 particles at a beginning part of the total particles used for the calculation, for example about one hundred (about 1%) particles, are implanted without taking an extended area into consideration, and a tracking calculation is performed until they become in the state of stopping. Then, statistics amount of “range Rp in the incident direction (called just a range Rp, hereafter)”, “standard deviation σL of a resting position perpendicular to the incident direction (called just a standard deviation σL, hereafter), etc. obtained from the calculation result of these n0 particles is calculated. It is assumed that these values are close to the result of implantation calculation using all n particles, an extended area which can cover ions implanted into an analysis area by slanting ion implantation without a gap is calculated and the extended area is defined to keep the amount of particles spilt out/in by scattering at the analysis area end to be almost balanced.
However, in this conventional technology, for example under the implantation conditions of high dose, it is impossible to accurately simulate the phenomenon that the Si (silicone) substrate becomes amorphous and channeling changes because of ions during the implantation. That is, when the statistics amount of the range Rp, the standard deviation σL, etc. obtained by using the n0 particles at the starting is different from that obtained from the calculation result of the implantation calculation using all the n particles, the set-up extended area is not suitable. Consequently, faults may arise that the rate of particles stopping still in the original calculation area becomes decreasing because the extended area is too large beyond necessity, or a distribution in which particles are spilt outside the calculation area end because the extended area is not extended enough to be a required size is obtained. Thus, for example under the implantation conditions of high dose, in the case a crystal structure of Si substrate turns to have an amorphous phenomenon and an amount of statistics calculated by some particles at the starting becomes different from what is obtained from a calculation result using all the n particles because of ions during the implantation, there is a problem that the accuracy of the calculation result is ruined as the set-up extended area is not suitable.
[Patent Document 1] Japanese Unexamined Patent Publication No. 6-84823 is a related art of the present invention.